Unified Pattern — Triple — without YANG, hexagram 27 (Dui, The Joyous — King Wen no. 58)
One of 256 distinct Unified Patterns — a 12×12 Jacquard construction where every cell's colour is read off a single hexagram of the Yi King, hexagram Dui, The Joyous. Binary numbering 0–63; in brackets, the traditional King Wen number.
Family Triple — without YANG, one of the 8 admissible families (out of 15) in the system's classification — see the lexicon for how families are built and admitted.
The pattern's three colour classes, set independently — change one, the other two stay put.
One tint, read in light and dark — a luminance reading, not three colours with two greyed out.
Reading the cell, line by line
The 144 cells of the 12×12 cell fall into six levels of 24 cells, one per line of the hexagram. Where the line is solid (yang), the level takes its colours from the family's YANG grid; where it is broken (yin), from its YANG mutant grid. Count of each colour, level by level:
| Level | Line | Grid read | Colour 1 (violet) | Colour 2 (magenta) | Colour 3 (orange) |
|---|---|---|---|---|---|
| 1 | solid | YANG | 8 | 8 | 8 |
| 2 | solid | YANG | 8 | 8 | 8 |
| 3 | broken | YANG mutant | 8 | 8 | 8 |
| 4 | solid | YANG | 8 | 8 | 8 |
| 5 | solid | YANG | 8 | 8 | 8 |
| 6 | broken | YANG mutant | 8 | 8 | 8 |
| Whole cell | 48 | 48 | 48 | ||
The three colours are exactly balanced: 48 cells each. The cell is unchanged by reflection in the diagonal, a half turn.
Hexagram 27 (King Wen no. 58) — The Joyous
Upper trigram ☱ Dui (The Joyous, the Lake); lower trigram ☱ Dui (The Joyous, the Lake).
Image
Lakes that join one another: the image of the joyous doubled. Two bodies of water communicate, nourishing one another, each amplifying the other's joy through their sheer proximity. This is the figure of sharing that multiplies rather than divides. Thus the noble one, with his friends, discusses and practices together: true joy, like the water of joined lakes, is never depleted by being shared — it is strengthened by it.
Judgement — Cadence
The clarity of the lake that gathers and holds in common. What gathers without constraint, by the sheer natural attraction of what it offers, creates the most lasting bonds. This line says true community is recognized by the lightness with which it forms.
The full hexagram page: the six lines, its magic square and the other patterns built on it.
Same shape, other colourings
Two involutions leave this motif's shape unchanged and only permute its three tints — verified across every family and every hexagram in the corpus, not just this one: swapping the pairing used to read the hexagram (YANG/YANG-mutant ↔ YIN/YIN-mutant), and taking the hexagram's binary complement (63 − 27 = 36). Toggle them below; the tiling never changes, only the colours do.
The grid itself
The 12×12 layer map and the three colour grids above, in the raw data — human-readable, and machine-readable as JSON.
Show the data
{
"famille": "par3:sans_yang",
"hexagramme": 27,
"complement_binaire": 36,
"layer_of": [
[
1,
1,
3,
4,
6,
6,
6,
6,
4,
3,
1,
1
],
[
1,
2,
2,
5,
5,
6,
6,
5,
5,
2,
2,
1
],
[
3,
2,
3,
4,
5,
4,
4,
5,
4,
3,
2,
3
],
[
4,
5,
4,
3,
2,
3,
3,
2,
3,
4,
5,
4
],
[
6,
5,
5,
2,
2,
1,
1,
2,
2,
5,
5,
6
],
[
6,
6,
4,
3,
1,
1,
1,
1,
3,
4,
6,
6
],
[
6,
6,
4,
3,
1,
1,
1,
1,
3,
4,
6,
6
],
[
6,
5,
5,
2,
2,
1,
1,
2,
2,
5,
5,
6
],
[
4,
5,
4,
3,
2,
3,
3,
2,
3,
4,
5,
4
],
[
3,
2,
3,
4,
5,
4,
4,
5,
4,
3,
2,
3
],
[
1,
2,
2,
5,
5,
6,
6,
5,
5,
2,
2,
1
],
[
1,
1,
3,
4,
6,
6,
6,
6,
4,
3,
1,
1
]
],
"grille_polarite_yang": [
[
"O",
"V",
"M",
"M",
"V",
"O",
"O",
"M",
"V",
"V",
"M",
"O"
],
[
"V",
"O",
"V",
"M",
"O",
"M",
"V",
"O",
"V",
"M",
"O",
"M"
],
[
"M",
"V",
"O",
"O",
"V",
"V",
"M",
"M",
"O",
"O",
"M",
"V"
],
[
"M",
"M",
"O",
"O",
"M",
"V",
"M",
"V",
"O",
"O",
"V",
"V"
],
[
"V",
"O",
"V",
"M",
"O",
"M",
"V",
"O",
"V",
"M",
"O",
"M"
],
[
"O",
"M",
"V",
"V",
"M",
"O",
"O",
"V",
"M",
"M",
"V",
"O"
],
[
"O",
"V",
"M",
"M",
"V",
"O",
"O",
"M",
"V",
"V",
"M",
"O"
],
[
"M",
"O",
"M",
"V",
"O",
"V",
"M",
"O",
"M",
"V",
"O",
"V"
],
[
"V",
"V",
"O",
"O",
"V",
"M",
"V",
"M",
"O",
"O",
"M",
"M"
],
[
"V",
"M",
"O",
"O",
"M",
"M",
"V",
"V",
"O",
"O",
"V",
"M"
],
[
"M",
"O",
"M",
"V",
"O",
"V",
"M",
"O",
"M",
"V",
"O",
"V"
],
[
"O",
"M",
"V",
"V",
"M",
"O",
"O",
"V",
"M",
"M",
"V",
"O"
]
],
"grille_polarite_yin": [
[
"M",
"O",
"V",
"V",
"O",
"M",
"M",
"V",
"O",
"O",
"V",
"M"
],
[
"O",
"M",
"O",
"V",
"M",
"V",
"O",
"M",
"O",
"V",
"M",
"V"
],
[
"V",
"O",
"M",
"M",
"O",
"O",
"V",
"V",
"M",
"M",
"V",
"O"
],
[
"V",
"V",
"M",
"M",
"V",
"O",
"V",
"O",
"M",
"M",
"O",
"O"
],
[
"O",
"M",
"O",
"V",
"M",
"V",
"O",
"M",
"O",
"V",
"M",
"V"
],
[
"M",
"V",
"O",
"O",
"V",
"M",
"M",
"O",
"V",
"V",
"O",
"M"
],
[
"M",
"O",
"V",
"V",
"O",
"M",
"M",
"V",
"O",
"O",
"V",
"M"
],
[
"V",
"M",
"V",
"O",
"M",
"O",
"V",
"M",
"V",
"O",
"M",
"O"
],
[
"O",
"O",
"M",
"M",
"O",
"V",
"O",
"V",
"M",
"M",
"V",
"V"
],
[
"O",
"V",
"M",
"M",
"V",
"V",
"O",
"O",
"M",
"M",
"O",
"V"
],
[
"V",
"M",
"V",
"O",
"M",
"O",
"V",
"M",
"V",
"O",
"M",
"O"
],
[
"M",
"V",
"O",
"O",
"V",
"M",
"M",
"O",
"V",
"V",
"O",
"M"
]
],
"grille_complement": [
[
"O",
"M",
"V",
"V",
"M",
"O",
"O",
"V",
"M",
"M",
"V",
"O"
],
[
"M",
"O",
"M",
"V",
"O",
"V",
"M",
"O",
"M",
"V",
"O",
"V"
],
[
"V",
"M",
"O",
"O",
"M",
"M",
"V",
"V",
"O",
"O",
"V",
"M"
],
[
"V",
"V",
"O",
"O",
"V",
"M",
"V",
"M",
"O",
"O",
"M",
"M"
],
[
"M",
"O",
"M",
"V",
"O",
"V",
"M",
"O",
"M",
"V",
"O",
"V"
],
[
"O",
"V",
"M",
"M",
"V",
"O",
"O",
"M",
"V",
"V",
"M",
"O"
],
[
"O",
"M",
"V",
"V",
"M",
"O",
"O",
"V",
"M",
"M",
"V",
"O"
],
[
"V",
"O",
"V",
"M",
"O",
"M",
"V",
"O",
"V",
"M",
"O",
"M"
],
[
"M",
"M",
"O",
"O",
"M",
"V",
"M",
"V",
"O",
"O",
"V",
"V"
],
[
"M",
"V",
"O",
"O",
"V",
"V",
"M",
"M",
"O",
"O",
"M",
"V"
],
[
"V",
"O",
"V",
"M",
"O",
"M",
"V",
"O",
"V",
"M",
"O",
"M"
],
[
"O",
"V",
"M",
"M",
"V",
"O",
"O",
"M",
"V",
"V",
"M",
"O"
]
]
}
Neighbouring motifs
The previous and next hexagram within the same family, Triple — without YANG.
